# Bonbons

Create a mixture of 50 kg of candy for a price of 700Kč. Candies have prices: 820Kč, 660Kč, and 580Kč. Use cross rule.

a =  15 kg
b =  30 kg
c =  5 kg

## Step-by-step explanation:

a+b+c=50
a=15
820a+660b+580c = 50·700

a+b+c=50
a=15
820·a+660·b+580·c = 50·700

a+b+c = 50
a = 15
820a+660b+580c = 35000

Pivot: Row 1 ↔ Row 3
820a+660b+580c = 35000
a = 15
a+b+c = 50

Row 2 - 1/820 · Row 1 → Row 2
820a+660b+580c = 35000
-0.805b-0.707c = -27.683
a+b+c = 50

Row 3 - 1/820 · Row 1 → Row 3
820a+660b+580c = 35000
-0.805b-0.707c = -27.683
0.195b+0.293c = 7.317

Row 3 - 0.19512195/-0.80487805 · Row 2 → Row 3
820a+660b+580c = 35000
-0.805b-0.707c = -27.683
0.121c = 0.606

c = 0.60606061/0.12121212 = 5
b = -27.68292683+0.70731707317073c/-0.80487805 = -27.68292683+0.70731707 · 5/-0.80487805 = 30
a = 35000-660b-580c/820 = 35000-660 · 30-580 · 5/820 = 15

a = 15
b = 30
c = 5

Our linear equations calculator calculates it.

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